Employment Law Questions? Ask an Employment Lawyer.
Legally, they would only have to pay you for the position once you started doing the position, not once you accepted the position.
In terms of your pay increase not valuing the position, unless the employer has a strictly written code or policy which outlines the exact pay for each position, such matters are left to employer discretion. There is no external law that would impose on an employer a specific pay.
You home address is not confidential in terms of employment law. I agree that they shouldn't be giving it out, but there isn't any statute that makes it a legal violation for the employer to do so.
The other complaints that you made, while perfectly valid as it pertains to a poor business model, also do not touch on issues of illegal actions by the employer against you that would allow for any sort of suit or action on your part against them.
I'm sorry that you have to face this situation and an employer that is not organized properly, but other than reporting the employer to their licensing committee to have their right to watch children questioned, I don't see any other action you can take here.